The invention relates to a method for determining amplitude and phase dependencies of RF pulses that, while passing through a defined k-space trajectory to produce an n-dimensional spatial pattern (n>=1) of the transverse magnetization, are irradiated into an object by means of at least one RF transmission antenna of a magnetic resonance measurement system (MR measurement system) as part of a spatially resolved magnetic resonance experiment.
Such a method is known, for example, from [6].
Magnetic resonance imaging (MRI), also known as magnetic resonance tomography (MRT), is a widely used technique for non-destructive acquisition of images of the interior of an object under examination and is based on the spatially resolved measurement of magnetic resonance signals from the object under examination. By subjecting the object under examination to an essentially static and homogeneous basic magnetic field within a basic field magnet, nuclear spins contained in it are oriented with respect to the direction of the basic field (usually the z-direction of a coordinate system referenced to the magnet). In the case of an MR examination, by irradiation of electromagnetic RF pulses by means of one or more RF transmission antennas, the nuclear spins of the object under examination thus oriented are excited into precession movements whose frequencies are proportional to the local magnetic field strengths. In the MRI methods generally used today, a spatial encoding for all three spatial directions is imposed on the precession movements of the nuclear spins by time-variable superposition of gradient fields GX, GY, and GZ, produced with a gradient system. This spatial encoding is usually described by a scheme in a space that is associated with physical space via a Fourier transform, called the k-space. The transverse component of the magnetization connected with the precessing nuclear spins induces voltage signals in one or more RF reception antennas that surround the object under examination. By means of pulse sequences that contain specially selected trains of RF pulses and gradient pulses, magnetic resonance signals that are variable over time are produced in such a way that they can be converted to the corresponding spatial mappings. This is performed according to one of many known reconstruction techniques by which the RF signals are acquired, amplified, and digitized by means of an electronic reception system, processed using an electronic computer system, and stored in two or three-dimensional datasets. The pulse train used typically contains a sequence of measurement operations in which the gradient pulses are varied according to the selected location method.
U.S. Pat. No. 7,078,899 B2 discloses an optimization method for k-space trajectories for use in MR imaging.
U.S. Pat. No. 5,758,646 A describes a method by which MR imaging sequences consisting of RF and gradient pulses are optimized with respect to important parameters (e.g. signal-to-noise ratio) to reduce the number of MR imaging sequences available for selection.
One important prerequisite for spatially accurate imaging of the nuclear spins of the object under examination is that the technical imperfections of the MR measurement system be negligible or that the deviations from the ideal behavior be known such that they can be corrected accordingly.
Spatially selective excitation is a widely used technique in magnetic resonance imaging that is used to spatially restrict the transverse magnetization produced during excitation and/or to vary its amplitude and phase in the excitation volume. In slice selection, the most frequent case of selective excitation, the excitation volume is reduced to a defined slice. Multidimensional selective excitation, in which the excitation volume is restricted in more than one direction or the excitation is modulated in more than one direction, has also produced numerous applications. These include the excitation of a small three-dimensional volume inside a much larger object under examination for localized spectroscopy, the mapping of a selectively excited region of interest (ROI) with a reduced field of view (FOV) for the purpose of shortening the measurement time, the excitation of special volumes adapted to structures of the object under examination, or also the echo-planar imaging with reduced echo train lengths. Moreover, amplitude and phase modulation during excitation can also be used to compensate for disadvantageous effects of an inhomogeneous B1 field of the RF antennas used for transmission. This is an application that has recently become vastly more important due to the large increases in high-field MRI systems.
In the past, spatially selective excitation was usually performed by means of a single RF transmission antenna with an essentially homogeneous transmission field (B1 field) in conjunction with the gradient system. Inspired by the success of parallel imaging, in which signal acquisition is performed with a configuration of multiple RF reception antennas, termed an antenna array in the technical literature, it has since become common practice to also deploy such arrays for transmission in selective excitation. This permits partial replacement of the spatial encoding that is implemented in selected excitation, by analogy with acquisition by varying gradient fields, by so-called sensitivity coding, thus reducing the length of the excitation pulses. This uses the information contained in the different spatial variations of the transmission profiles of the individual array elements, hereafter also termed transmission profiles. Because the length of such selective excitation pulses has usually been one of the limiting criteria for the applicability of this technique, parallel excitation (PEX) is a promising method to enable wider use of spatially selective excitation than has so far been possible.
One of the basic questions in the deployment of spatially selective excitation is the determination of the RF pulses that have to be emitted by the RF transmission system to generate the desired excitation pattern in conjunction with the k-space trajectory produced by the gradients. In the article “A k-space analysis of small tip-angle excitation” [1], Pauly et al. describe a method for one-channel spatially selective excitation with which the sought pulse shape B1 (t) can be calculated based on a mathematical analogy of the selective excitation with Fourier imaging essentially by means of a Fourier transform of the desired excitation pattern and sampling of the Fourier-transform along the defined k-space trajectory. Katscher et al. extended this calculation method to the case of an antenna array with multiple independent transmission channels [2].
However, the decisive disadvantage of the calculation methods described in these articles is that diverse experimental factors that can negatively influence accurate implementation of the excitation and manifest themselves in artifacts, depending on the specific k-space trajectory, are not or cannot be taken into account in the calculation. One example of such influencing factors are inhomogeneities of the basic magnetic field that cause the resonance frequency of the nuclear spins to no longer match the irradiated RF frequency at certain locations of the object under examination (causing off-resonances). Further factors include the relaxation of the spin system during the pulses and the deviation of the real k-space trajectory from its theoretical form defined in the calculation because of technical imperfections of the gradient system and physical interference factors such as induced eddy currents.
As a result of these disadvantages, further methods for pulse calculation for spatially selective excitation have gradually come about. In some works [3, 4], the conjugate-phase (CP) method from image reconstruction was used, which can take off-resonance effects into account and correct them to some degree. Despite the CP method's ability to correct off-resonance effects, these conventional methods for pulse calculation are less than optimal in a number of respects. The algorithms generally result in pulses that do not optimally achieve accurate implementation of the desired excitation pattern, in particular, if the k-space trajectory exhibits a degree of under-sampling or if the off-resonance influences exhibit pronounced spatial variation. A more recent method for pulse calculation introduced by Yip et al. [5] and generalized for multi-channel transmission by Grissom et al. [6], is based on an optimization method and achieves improvements in excitation accuracy in two respects. On the one hand, it is more robust than under-sampling the k-space, on the other hand, it is a simple way of taking off-resonance influences into account in pulse calculation. Moreover, it provides the possibility of including further constraints in the calculation, such as control of the integrated or also the maximum RF transmission power, which is important for SAR (specific absorption rate) control or technical restrictions on the RF power transmitters.
A general additional problem with these new methods is that relatively precise maps of the basic magnetic field variations have to be initially acquired in the region of the object under examination in order to correct for off-resonance effects. This is often difficult, especially in in-vivo conditions. To also compensate for effects of transverse relaxation in pre-calculation with these methods, which is possible in theory although not explicitly mentioned in the relevant publications, detailed determination of the spatial dependence of the T2* relaxation times within the object under examination is also required in this case.
A further problem that is not taken into account in the stated calculation methods at all is the deviations of the actual k-space trajectory produced by the gradients from the theoretical trajectory.
The object of this invention is therefore to provide a method for determining amplitude and phase dependencies of RF pulses for one or mufti-channel spatially selective excitation, in which the experimental imperfections addressed are taken into account and intrinsically compensated for irrespective of whether they are caused by the object under examination or physical and technical constraints of the system.